Volume 7, Issue 5
Existence, Uniqueness and Fourth-Order Numerical Method for Solving Fully Third-Order Nonlinear ODE with Integral Boundary Conditions

Dang Quang A & Dang Quang Long

J. Nonl. Mod. Anal., 7 (2025), pp. 1886-1904.

Published online: 2025-09

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we establish the existence, uniqueness and construct fourth-order numerical method for solving fully third-order nonlinear differential equation with integral boundary conditions. The method is based on the discretization of an iterative method on continuous level with the use of the trapezoidal quadrature formulas with corrections. Some examples demonstrate the applicability of the theoretical results of existence and uniqueness of solution and the fourth-order convergence of the proposed numerical method. The approach used for the third-order nonlinear differential equation with integral boundary conditions can be applied to differential equations of any order.

  • AMS Subject Headings

34B15, 34L30, 65L10, 65L12

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COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1886, author = {A , Dang Quang and Long , Dang Quang}, title = {Existence, Uniqueness and Fourth-Order Numerical Method for Solving Fully Third-Order Nonlinear ODE with Integral Boundary Conditions}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {5}, pages = {1886--1904}, abstract = {

In this paper, we establish the existence, uniqueness and construct fourth-order numerical method for solving fully third-order nonlinear differential equation with integral boundary conditions. The method is based on the discretization of an iterative method on continuous level with the use of the trapezoidal quadrature formulas with corrections. Some examples demonstrate the applicability of the theoretical results of existence and uniqueness of solution and the fourth-order convergence of the proposed numerical method. The approach used for the third-order nonlinear differential equation with integral boundary conditions can be applied to differential equations of any order.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1886}, url = {http://global-sci.org/intro/article_detail/jnma/24396.html} }
TY - JOUR T1 - Existence, Uniqueness and Fourth-Order Numerical Method for Solving Fully Third-Order Nonlinear ODE with Integral Boundary Conditions AU - A , Dang Quang AU - Long , Dang Quang JO - Journal of Nonlinear Modeling and Analysis VL - 5 SP - 1886 EP - 1904 PY - 2025 DA - 2025/09 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1886 UR - https://global-sci.org/intro/article_detail/jnma/24396.html KW - Third-order nonlinear differential equation, integral boundary conditions, iterative method, fourth-order convergence. AB -

In this paper, we establish the existence, uniqueness and construct fourth-order numerical method for solving fully third-order nonlinear differential equation with integral boundary conditions. The method is based on the discretization of an iterative method on continuous level with the use of the trapezoidal quadrature formulas with corrections. Some examples demonstrate the applicability of the theoretical results of existence and uniqueness of solution and the fourth-order convergence of the proposed numerical method. The approach used for the third-order nonlinear differential equation with integral boundary conditions can be applied to differential equations of any order.

A , Dang Quang and Long , Dang Quang. (2025). Existence, Uniqueness and Fourth-Order Numerical Method for Solving Fully Third-Order Nonlinear ODE with Integral Boundary Conditions. Journal of Nonlinear Modeling and Analysis. 7 (5). 1886-1904. doi:10.12150/jnma.2025.1886
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